Integrated drive and readout circuit for superconducting qubits

ABSTRACT

Embodiments of the present invention are directed to an integrated drive and readout circuit assembly. Directional couplers are configured to connect to qubit-resonator systems. Diplexers are coupled to the directional couplers. A microwave signal combiner is coupled to the diplexers.

DOMESTIC PRIORITY

This application claims priority to U.S. application Ser. No.15/478,906, entitled “INTEGRATED DRIVE AND READOUT CIRCUIT FORSUPERCONDUCTING QUBITS”, filed Apr. 4, 2017, which is incorporatedherein by reference in its entirety.

BACKGROUND

The present invention relates generally to superconducting electronicdevices, and more specifically, to integrated drive and readout circuitsfor superconducting qubits.

The fundamental element of a quantum computer is the quantum bit whichis known as the “qubit.” As opposed to a classical bit representing zeroand one, a qubit is also able to represent a quantum superposition ofthe two states. The states can be formalized within the laws of quantumphysics as a probability of being in the two states. Accordingly, thestates can be manipulated and observed within the laws of quantumphysics.

In cavity quantum electrodynamics, quantum computing employs nonlinearsuperconducting devices (i.e., qubits) to manipulate and store quantuminformation at microwave frequencies, and resonators (e.g., as atwo-dimensional (2D) planar waveguide or as a three-dimensional (3D)microwave cavity) to read out and facilitate interaction among qubits.As one example, each superconducting qubit can include one or moreJosephson junctions shunted by capacitors in parallel with thejunctions. The qubits are capacitively coupled to resonators such as,for example, 2D or 3D microwave cavities).

The electromagnetic energy associated with the qubit is stored in theJosephson junctions and in the capacitive and inductive elements formingthe qubit. In one example, to read out the qubit state, a microwavesignal is applied to the microwave readout cavity that couples to thequbit at the cavity frequency corresponding to the qubit state. Thetransmitted (or reflected) microwave signal goes through multiplethermal isolation stages and low-noise amplifiers that are required toblock or reduce the noise and improve the signal-to-noise ratio. Themicrowave signal is measured at room temperature. The amplitude or phaseof the readout microwave signal (or both) can, depending on the readoutscheme, carry information about the qubit state. This readout signal canbe measured and analyzed using room-temperature electronics. Microwavereadout provides a stable signal amplitude for control, and commercialoff-the-shelf (COTS) hardware is available to use.

Quantum systems such as superconducting qubits are very sensitive toelectromagnetic noise, particularly in the microwave and infrareddomains. In order to protect these quantum systems from microwave andinfrared noise, several layers of filtering, attenuation, and isolationare applied. Particular interest is directed to the layers of protectionemployed on the input and output (I/O) lines, which are also calledtransmission lines. The I/O lines (transmission lines) are connected tothe quantum system and carry the input and output signals to and fromthe quantum system respectively. In the case of superconducting qubits,these I/O lines (transmission lines) are usually microwave coaxial linesor waveguides. Some of the techniques or components that are used inorder to block or attenuate the noise propagating or leaking into thesetransmission lines are attenuators, circulators, isolators, low-passmicrowave filters, bandpass microwave filters, and infrared filterswhich are based on lossy absorptive materials or dispersive elements. Anintegrated drive and readout circuit is needed to drive and readout thesuperconducting qubits with a minimum number of input and outputtransmission lines and minimum number of components.

SUMMARY

Embodiments of the present invention are directed to an integrated driveand readout circuit assembly. A non-limiting example of the integrateddrive and readout circuit assembly includes directional couplersconfigured to connect to qubit-resonator systems, diplexers coupled tothe directional couplers, and a microwave signal combiner coupled to thediplexers.

Embodiments of the present invention are directed to a method of formingan integrated drive and readout circuit assembly. A non-limiting exampleof the method includes providing directional couplers configured toconnect to qubit-resonator systems, coupling diplexers to thedirectional couplers, and coupling a microwave signal combiner to thediplexers.

Embodiments of the present invention are directed to a chip. Anon-limiting example of the chip includes directional couplersconfigured to connect to qubit-resonator systems, diplexers coupled tothe directional couplers, and a microwave signal combiner coupled to thediplexers.

Embodiments of the present invention are directed to a method of drivingqubit-resonator systems. A non-limiting example of the method includestransmitting, by directional couplers, microwave signals to thequbit-resonator systems, receiving back, by the directional couplers,the microwave signals having been reflected from the qubit-resonatorsystems, and receiving, by diplexers, the microwave signals from thedirectional couplers. The diplexers are configured to direct themicrowave signals to a termination.

Embodiments of the present invention are directed to a method of readingout qubit-resonator systems. A non-limiting example of the methodincludes transmitting, by directional couplers, microwave signals to thequbit-resonator systems, receiving back, by the directional couplers,the microwave signals having been reflected from the qubit-resonatorsystems, and receiving, by diplexers, the microwave signals from thedirectional couplers, receiving, by a microwave signal combiner, themicrowave signals from the diplexers. The microwave signal combiner isconfigured to combine the microwave signals into combined microwavesignals. Also, the method includes transmitting, by the microwave signalcombiner, the combined microwave signals to a quantum-limited amplifier.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic of an integrated drive and readout circuitillustrating readout of superconducting qubits according to embodimentsof the present invention.

FIG. 2 is a schematic of the integrated drive and readout circuitillustrating driving the superconducting qubits according to embodimentsof the present invention.

FIG. 3 is a schematic of an integrated drive and readout circuitaccording to embodiments of the present invention.

FIG. 4 is a schematic of a signal combiner according to embodiments ofthe present invention.

FIG. 5 is a schematic of a signal combiner according to embodiments ofthe present invention.

FIG. 6 is a flow chart of a method of forming an integrated drive andreadout circuit according to embodiments of the present invention.

FIG. 7 is flow chart of a method of driving qubit-resonator systemsaccording to embodiments of the present invention.

FIG. 8 is a flow chart of a method of reading out qubit-resonatorsystems according to embodiments of the present invention.

DETAILED DESCRIPTION

Various embodiments of the present invention are described herein withreference to the related drawings. Alternative embodiments of thepresent invention can be devised without departing from the scope ofthis document. It is noted that various connections and positionalrelationships (e.g., over, below, adjacent, etc.) are set forth betweenelements in the following description and in the drawings. Theseconnections and/or positional relationships, unless specified otherwise,can be direct or indirect, and are not intended to be limiting in thisrespect. Accordingly, a coupling of entities can refer to either adirect or an indirect coupling, and a positional relationship betweenentities can be a direct or indirect positional relationship. As anexample of an indirect positional relationship, references to forminglayer “A” over layer “B” include situations in which one or moreintermediate layers (e.g., layer “C”) is between layer “A” and layer “B”as long as the relevant characteristics and functionalities of layer “A”and layer “B” are not substantially changed by the intermediatelayer(s).

Several physical objects have been suggested as potentialimplementations of qubits. However, solid-state circuits, andsuperconducting circuits in particular, are of great interest as theyoffer scalability which is the possibility of making circuits with alarger number of interacting qubits. Superconducting qubits aretypically based on Josephson junctions (JJ). A Josephson junction is twosuperconductors coupled by, for example, a thin insulating barrier. AJosephson junction can be fabricated by means of an insulating tunnelbarrier, such as Al₂O₃, between superconducting electrodes. For suchJosephson junctions, the maximum allowed supercurrent is the criticalcurrent I_(c).

Embodiments are configured to build a scalable qubit drive and readoutcircuit that minimizes the number of output lines and control lines ofthe circuit. Embodiments provide techniques to build a scalable qubitdrive and readout circuit which can be integrated together on the samecircuit board or chip.

Additionally, embodiments are configured to minimize the number ofcirculators and isolators. Embodiments further provided a scalable qubitdrive and readout circuit that can be optimized, replaced, andthermalized well. To emphasize the size/space of circulators andisolators, the size of a commercial cryogenic isolator is about 8.5centimeters (cm)×3.1 cm×1.7 cm, and it weighs about 229.5 grams (g). Acopper bracket is used to thermalize the cryogenic isolator weighs about183.1 g. The size of a commercial cryogenic circulator is about 4.5cm×3.5 cm×1.8 cm, and it weighs about 41.2 g. In a standard 1 input 1output line setup, which connects 1 qubit-resonator and 1quantum-limited amplifier (JPC), the state-of-the-art uses twocirculators and three isolators. This accounts for a volume of at least191.1 cm³ and weight of at least 1.5 kg (and this weight is just fromthe circulators and isolators). The volume calculation does not takeinto account the weight of the copper brackets that are used forthermalization. In contrast, embodiments provide a structure with 1output line and 1 (optional) circulator/isolator.

Now turning to the figures, FIG. 1 is a schematic of an integrated driveand readout circuit assembly 100 illustrating readout of superconductingqubits according to embodiments. FIG. 2 is a schematic of the integrateddrive and readout circuit 100 illustrating driving the superconductingqubits according to embodiments. The system in FIGS. 1 and 2 areidentical and illustrate a difference in operation (i.e., reading thequbits versus driving the qubits respectively) of the circuits 100.FIGS. 1 and 2 (along with FIG. 3) apply to qubit-resonator systemsoperating in reflection as understood by one skilled in the art.

The circuit 100 can be implemented on chip and/or on a printed circuitboard and/or as an integrated circuit. For example, the integrated driveand readout circuit 100 can be a chip. The circuit 100 is operativelyconnected to quantum systems. A quantum system is a superconductingqubit coupled to a readout resonator such that the superconducting qubitcan be driven (i.e., driven to an excited state or a superposition ofground and excited states) and read out. The read out of the state ofthe qubit is by measuring the readout resonator. There arequbit-resonator systems 102_1 through 102_N, where N corresponds to thelast number of qubit-resonator systems. Each qubit-resonator systems102_1 through 102_N has its own superconducting qubit coupled to areadout resonator. For example, the qubit-resonator systems 102_1through 102_N respectively have superconducting qubits 154_1 through154_N and respectively have readout resonator 152_1 through 152_N. Asnoted above, readout resonators can be implemented as lumped-elementresonators, microstrip/stripline resonators, coplanar waveguideresonators, 3D microwave cavities, etc.

The integrated drive and readout circuit 100 includes widebanddirectional couplers 104_1 through 104_N operatively connected to thequbit-resonator systems 102_1 through 102_N, respectively. The circuit100 includes diplexers 106_1 through 106_N operatively connected to thewideband directional couplers 104_1 through 104_N, respectively. Asignal combiner 108 is operatively connected to each of the diplexers106_1 through 106_N such that the signal combiner 108 receives inputfrom the diplexers 106_1 through 106_N. Optionally, the circuit 100 caninclude a wideband quantum-limited directional amplifier 110 having itsinput operatively connected to the output of the signal combiner 108.Optionally, the circuit 100 can include a wideband on-chip 4-portcirculator 112 or a wideband isolator, which is connected to the outputof the wideband quantum-limited directional amplifier 110. The widebandquantum-limited directional amplifier 110 and the wideband on-chip4-port circulator 112 can optionally be on-chip which means on thechip/circuit 100 or off-chip. FIG. 3 is an example of the widebandquantum-limited directional amplifier 110 and the wideband on-chip4-port circulator 112 being off-chip.

According to embodiments, the scalable qubit drive and readout circuit100 is used to drive and measure an array of circuit quantumelectrodynamics systems (such as superconducting cavity/readoutresonator-qubit systems 102_1 through 102_N) which are driven andmeasured in reflection. The superconducting cavity/readoutresonator-qubit systems 102_1 through 102_N are depicted for explanationpurposes. It should be appreciated that this drive and readoutcircuit/scheme is not limited to superconducting qubits. It can be usedwith any type of qubits coupled to microwave resonators (i.e., anyquantum system). One condition is that the qubit drive signals andreadout signal are fed to the same port of the quantum system.

Now turning to the components of the circuit assembly 100 in moredetail, the wideband directional couplers 104_1 through 104_N have afrequency band that covers (i.e., encompasses) the frequency range ofboth qubits (i.e., qubits 154 and readout resonators 152). The widebanddirectional couplers 104_1 through 104_N are 4-port devices with ports103A, 103B, 103C, and 103D. Couplers are configured to couple a definedamount of electromagnetic power of a signal from a certain port toanother port thereby enabling the signal to be used in another circuit.Only the directional coupler 104_1 is labeled with ports 103A-103D so asnot to obscure the figures. However, it should be appreciated that theother directional couplers 104_2 through 104_N analogously have the sameports and operate the same as the directional coupler 104_1 having itsports labeled for ease of understanding.

The drive signals and readout signals are fed through the coupled port103A of the directional couplers 104_1 through 104_N. The isolated port103D of the directional coupler 104_2 through 104_N is terminated by a50 ohm (Ω) termination. The 50 ohm Ω termination can be either on-chipor an external 50Ω termination. The 50Ω termination can be a load, suchas a resistive load. The input port 103B of the directional coupler104_1 through 104_N is connected to the qubit-readout resonator systems102_1 through 102_N. The attenuation of the signals (drive signalsand/or readout signals) coupling from the coupled port 103A to the inputport 103B is between 10-30 decibels (dB).

The output port 103C of the directional coupler 104_1 through 104_N isconnected to on-chip diplexers 106_1 through 106_2. The purpose of thediplexers 106_1 through 106_2 is to direct the reflected qubit pulses(i.e., reflected drive signals) to the 50Ω termination (on chip orexternal) so that the reflected qubit pulses are dissipated, whilepassing the reflected readout signals toward the output line/chain(OUT). The different readout signals which pass through the differentdiplexers 106_1 through 106_N are combined using the signal combiner 108for quantum signals (i.e., the reflected readout signals), and thesignal combiner 108 uses frequency division multiplexing to combine thedifferent (reflected) readout signals onto a single transmission linecarrying readout signal at frequencies f₁, f₂, . . . f_(N). The readoutsignals can be applied in series, in parallel, or in any combination.The different combined readout signals at frequencies f₂, . . . f_(N)are output from the signal combiner 108 to the wideband directionalamplifier 110. The wideband directional amplifier 110 amplifies thecombined readout signals at frequencies f₁, f₂, . . . f_(N). Thewideband directional amplifier 110 can be followed by an on-chipcirculator 112 or isolator which protects the quantum systems (such asthe qubit-cavity/readout resonator systems 102_1 through 102_N) fromnoise coming down from the output chain (i.e., OUT). The on-chipcirculator 112 or isolator can be realized by using three-wave mixingdevices (for example, Josephson parametric converters) and hybrids or byusing ferrites and permanent magnets.

As an example of driving a qubit-resonator in FIG. 2, the followingscenario explains driving the qubit-resonator system 102_1 having thereadout resonator 152_1 and superconducting qubit 154_1 but applies byanalogy to driving the qubit-resonator system 102_2 through 102_N havingreadout resonators 152_2 through 152_N and superconducting qubits 154_2through 154_N, respectively. The qubit-resonator system 102_1,directional coupler 104_1, and diplexer 106_1 are all in a one-to-onerelationship.

Each of the qubit-resonator system 102_1 through 102_N can be drivensimultaneously, nearly simultaneously, and/or in series. Each of thequbits 154_1 through 154_N has its resonance frequency which can bereferred as a qubit frequency or qubit resonance frequency. For example,the qubits 154_1 through 154_N have qubit resonance frequencies f_(q1)through f_(qN) respectively, where N is the last number. Thesefrequencies can be the same or different (i.e., close to each other, forexample a few megahertz, or far from each other, for example a fewhundreds of megahertz), depending on the particular implementationscheme of the quantum processer. In the example scenario of driving thequbit-resonator system 102_1, the qubit 154_1 has the qubit resonancefrequency f_(q1). Accordingly, a (drive) microwave signal (tone) at thefrequency f_(q1) is input into the coupled port 103A of the widebanddirectional coupler 104_1 with the purpose of driving/manipulating thequbit 154_1 to the desired state. The wideband directional coupler 104_1couples a portion of the microwave drive signal (for example 1%) at thefrequency f_(q1) to port 103B of the wideband directional coupler 104_1and dissipates the remainder (or nearly all of the remainder) of themicrowave drive signal at f_(q1) at the isolated port 103D (connected toa 50Ω cold termination). The drive microwave signal at the frequencyf_(q1) is input to the qubit-resonator system 102_1 and causes the qubit154_1 to resonate because the drive microwave signal at the frequencyf_(q1) matches or nearly matches the qubit resonance frequency f_(q1) ofthe qubit 154_1. The reflected microwave signal at frequency f_(q1) offthe qubit-resonator system 102_1 enters the input port 103B of thewideband directional coupler 104_1 and most of the signal (for example99%) leaves through port 103C. The wideband directional coupler 104_1 isconfigured to output the reflected (drive) microwave signal at frequencyf_(q1) to the common port 105A of the diplexer 106_1. The diplexer 106_1(along with diplexers 106_2 through 106_N) has a low-pass filterconnected to port 105B and a high-pass filter connected to port 105C.The low-pass filter is designed to pass the reflected drive microwavesignal at frequency f_(q1) to port 105B, such that the reflected drivemicrowave signal at frequency f_(q1) is dissipated by the 50Ω coldtermination. Typically, the different qubit resonance frequencies f_(q1)through f_(qN) for the respective qubits 154_1 through 154_N are in thefrequency range of about 3.5-5.5 gigahertz (GHz). Accordingly, the drivemicrowave signals and the corresponding reflected drive microwavesignals (for qubits 154_1 through 154_N) are in the frequency range ofabout 3.5-5.5 gigahertz (GHz). The low-pass filter in each of thediplexers 106_1 through 106_N is designed to pass the reflected drivemicrowave signals at qubit resonance frequencies f_(q1) through f_(qN)for the respective qubits 154_1 through 154_N, such that none of thequbit resonance frequencies f_(q1) through f_(qN) for the respectivequbits 154_1 through 154_N reach the signal combiner 108. In someimplementations, the low-pass filters can be designed to passfrequencies below 5.6 GHz in order to pass the qubit frequencies in thefrequency range of about 3.5-5.5 gigahertz. In other implementations,when the qubit resonance frequencies f_(q1) through f_(qN) are less than5.0 GHz, the low-pass filters can be designed to pass frequencies below5 GHz to the port 105B to the 50Ω cold termination.

If the reflected drive microwave signals at qubit resonance frequenciesf_(q1) through f_(qN) were not dissipated by the diplexers 106_1 through106_N, the signal combiner 108 would reject the qubit resonancefrequencies f_(q1) through f_(qN), and therefore, these rejected signalswould be reflected back to the qubit-resonator system 102_1 through102_N. This is an unwanted situation and is avoided by having thelow-pass filter at port 105B and by having the high pass filter at port105C that rejects qubit resonance frequencies f_(q1) through f_(qN).

The diplexers 106_1 through 106_N are 3-port devices with ports 105A,105B, and 105C. Only the diplexer 106_1 is labeled with ports 105A-105Cso as not to obscure the figures. However, it should be appreciated thatthe other diplexers 106_2 through 106_N analogously have the same portsand operate the same as the diplexer 106_1 having its ports labeled.

Returning to the example scenario of driving the qubit 154_1 inqubit-resonator system 102_1, the reflected drive microwave signal atfrequency f_(q1) has been dissipated and driving the qubit 154_1 inqubit-resonator system 102_1 is complete. This same driving processdiscussed for qubit 154_1 in qubit-resonator system 102_1 applies todriving the qubits 154_2 through 154_N in qubit-resonator system 102_2through 102_N but with respective qubit resonance frequencies f_(q2)through f_(qN) and the respective input line.

As an example of readout of a qubit-resonator in FIG. 1, the followingscenario explains reading out the qubit-resonator system 102_1 havingthe readout resonator 152_1 and superconducting qubit 154_1 but appliesby analogy to reading out the qubit-resonator systems 102_2 through102_N having readout resonators 152_2 through 152_N and superconductingqubits 154_2 through 154_N, respectively. The state of each of thequbits 154_1 through 154_N can be read out simultaneously or nearlysimultaneously by reading out the respective readout resonators 152_1through 152_N. Each of the readout resonators 152_1 through 152_N hasits own resonance frequency, which can be referred to as a readoutresonator frequency or readout resonator resonance frequency. Forexample, the readout resonators 152_1 through 152_N have (different)readout resonator resonance frequencies f₁ through f_(N) respectively,where N is the last number. In the example scenario of reading out thereadout resonator 152_1 in qubit-resonator system 102_1, the readoutresonator 152_1 has the readout resonator resonance frequency f₁.Accordingly, a (readout) microwave signal (tone) at the frequency f₁ isinput into the coupled port 103A of the wideband directional coupler104_1 with the purpose of reading out the readout resonator 152_1. Thewideband directional coupler 104_1 couples a portion of the microwavereadout signal at f₁ to port 103B of the wideband directional coupler104_1 and dissipates the remainder (or nearly all the remainder) of thereadout signal at frequency f₁ at the isolated port 103D (connected to a50Ω cold termination). The readout microwave signal at the frequency f₁is input to the qubit-resonator system 102_1. At this point, the processfor inputting the drive microwave signal and readout microwave signal isthe same. However, being input to the qubit-resonator system 102_1, thereadout microwave signal at the frequency f₁ causes the readoutresonator 152_1 to resonate because the readout microwave signal at thefrequency f₁ is matches or nearly matches the readout resonatorresonance frequency f₁ of the readout resonator 152_1. By having thereadout microwave signal at frequency f₁ on resonance with the readoutresonator 152_1, this causes the readout resonator 152_1 to transmit areflected (readout resonator) microwave signal at frequency f₁. Thereflected readout microwave signal at frequency f₁ is output from thequbit-resonator system 102_1 back to the input port 103B of the widebanddirectional coupler 104_1. The wideband directional coupler 104_1 isconfigured to output most of the reflected readout microwave signal atfrequency f₁ to the output port of 103C of the directional coupler 104_1and afterwards to the common port 105A of the diplexer 106_1. Thediplexer 106_1 (along with diplexers 106_2 through 106_N) has thelow-pass filter at port 105B and the high-pass filter at port 105C. Thehigh-pass filter is designed to pass the reflected readout resonatormicrowave signal at frequency f₁ through port 105C to port 107_1 of thesignal combiner 108, while blocking reflected qubit microwave signal atfrequency f₁. Typically, the different readout resonance frequencies f₁through f_(N) for the respective readout resonator 152_1 through 152_Nare in the frequency range of about 6 GHz or higher. The readoutresonators 152_1 through 152_N are designed to have different resonancefrequencies. The high-pass filter in each of the diplexers 106_1 through106_N is designed to pass the respective reflected readout microwavesignals at the readout resonance frequencies f₁ through f_(N) for therespective readout resonators 152_1 through 152_N, such that each of thereadout resonance frequencies f₁ through f_(N) for the readoutresonators 152_1 through 152_N reach the signal combiner 108. Forexample, the high-pass filters can be designed to pass frequencies above6 GHz.

Example details of the diplexers 106_1 through 106_N have beenillustrated for explanation purposes, but implementation of thediplexers 106_1 through 106_N is not meant to be limited. For example,the diplexers 106_1 through 106_N do not necessarily have to use alow-pass filter and high-pass filter. In other implementations, thediplexers 106_1 through 106_N can use band-pass filters in which onebandpass filter that transmits in the range of the qubit frequencies(f_(q1) through f_(qN).) is connected to port 105B and another bandpassfilter that transmits in the range of the readout frequencies (f₁through f_(N)) is connected to 105C.

Returning to the example scenario of reading out the readout resonator152_1 in qubit-resonator system 102_1, the reflected readout microwavesignal at frequency f₁ has been input to port 107_1 of the signalcombiner 108. The signal combiner 108 is configured to combine themicrowave signal at frequency f₁ from readout resonator 152_1 with thereadout microwave signals at frequency f₂ through f_(N) from readoutresonators 152_2 through 152_N (which have been similarly input viaports 107_2 through 107_N). The combined reflected microwave signals atfrequencies f₁ through f_(N) are then output from the port 109 of thesignal combiner 108 to the wideband quantum-limited directionalamplifier 110. The amplifier 110 is configured to amplify the combinedreflected microwave signal of frequencies f₁ through f_(N). Theamplifier 110 is designed to amplify within a bandwidth that coversreadout frequencies f₁ through f_(N). The amplified microwave signals offrequencies f₁ through f_(N) is output to a wideband circulator 112 thatpasses the combined reflected microwave signals of frequencies f₁through f_(N) to a transmission line designated as OUT.

This same readout process discussed for readout resonator 152_1 inqubit-resonator system 102_1 applies to reading out the readoutresonators 152_2 through 152_N in qubit-resonator system 102_2 through102_N but with respective readout resonator resonance frequencies f₂through f_(N).

According to embodiments, the integrated drive and readout circuit 100provides many benefits. The circuit 100 can be fully integrated on achip or printed circuit board. The circuit 100 minimizes the number ofoutput lines (OUT) and control lines. A control line would only beneeded for the quantum-limited amplifier 110 if the quantum-limitedamplifier 110 is on the chip 100, and FIG. 3 illustrates an examplewhere the quantum-limited amplifier 110 is not on the chip 100. Allcomponents (e.g., are passive and do not require any control lines thatcarry drives or control signals with the exception of the directionalamplifier (i.e., quantum-limited amplifier 100) and the on-chipcirculator/isolator (e.g., circulator 112). The drive and readouttechnique with circuit 100 does not require the use of off-chipcirculators or isolators. This integrated circuit 100 can be thermalizedwell because the circuit 100 does not require the large number ofcirculators/isolators as would be needed in the state-of-the-art. Forexample, for each one of the N qubit-resonator systems 102, thestate-of-the-art high-fidelity measurement scheme requires twocirculators (assuming the use of a Josephson parametric amplifier in theoutput chain) and three isolators per qubit-resonator system.Accordingly, the technique using the circuit 100 can have lighter weightand smaller footprint in embodiments than state-of-the-art approacheswhich incorporate commercial cryogenic circulators and isolators.Further, the circuit 100 can have a low insertion loss, for example,less than (<) 2 decibels (dB) as it can be implemented usingsuperconducting circuits or very low-loss normal metal, and low-lossdielectric components. The low-loss requirement is needed in order tominimize the loss of quantum information in the output chain.

FIG. 3 is a schematic of an integrated drive and readout circuitassembly 100 according to embodiments. In FIG. 3, fewer circuit elementsare depicted on the integrated circuit 100 than in FIGS. 1 and 2. FIG. 3illustrates the integrated circuit 100 having the wideband directionalcouplers 104_1 through 104_N, the diplexers 106_1 through 106_N, and thesignal combiner 108. FIG. 3 does not have the quantum-limiteddirectional amplifier 110 and the circulator 112 on chip. FIG. 3illustrates an example with a quantum processor 300 operativelyconnected to the integrated circuit 100. The drive and readout operationin FIG. 3 is identical to that explained in FIGS. 1 and 2.

FIG. 4 is a schematic of the signal combiner 108 for combining quantumsignals (i.e., microwave signals) according to embodiments. The signalcombiner 108 is configured to utilize frequency division multiplexing toallocate different frequencies for different microwave signals onto asingle output transmission line. The signal combiner 108 includesbandpass microwave filters generally referred to as bandpass filters405. The different bandpass filters 405 are depicted as bandpass filters405_1 through bandpass filters 405_N. Each bandpass filter 405 has adifferent narrow passband through which microwave signals having afrequency in the particular narrow passband are transmitted (i.e.,passed) and signals having a frequency outside of the particular narrowpassband are reflected (i.e., blocked). The bandpass filter 405_1 hasits own narrow passband with a bandwidth 1 (BW₁), bandpass filter 405_2has its own narrow passband with a bandwidth 2 (BW₂), and bandpassfilter 405_N has its own narrow passband with a bandwidth N (BW_(N)).

For example, bandpass filter 405_1 is configured with a passband(frequency band) that permits a (reflected readout) microwave signal305_1 having frequency f₁ (corresponding to the readout resonator 152_1)to pass (transmit) through but blocks (reflects) all other microwavesignals 305_2 through 305_N having frequencies f₂ through f_(N) whichare outside of the passband for bandpass filter 405_1. Similarly,bandpass filter 405_2 is configured with a passband (frequency band)that permits a (reflected readout) microwave signal 305_2 havingfrequency f₂ (corresponding to the readout resonator 152_2) to pass(transmit) through but blocks (reflects) all other microwave signals305_1, 305_3 through 305_N having frequencies f₁, f₃ through f_(N) whichare outside of the passband for bandpass filter 405_2. Analogously,bandpass filter 405_N is configured with a passband (frequency band)that permits a (reflected readout) microwave signal 305_N havingfrequency f_(N) (corresponding to readout resonator 152_N) to pass(transmit) through but blocks (reflects) all other microwave signals305_1 through 305_N−1 having frequencies f₁ through f_(N-1) which areoutside of the passband for bandpass filter 405_N. The microwave signals305_1 through 305_N are generally referred to as microwave signals 305.When qubit-resonator quantum systems 102_1 through 102_N are operativelyconnected to the signal combiner 108, the microwave signals 305 can beat respective frequencies f₁ through f_(N) designated to readout qubit(via readout resonators or cavities), as understood by one skilled inthe art.

The signal combiner 108 includes ports 107_1 through 107_N individuallyconnected to respective bandpass filters 405_1 through 405_N. In thesignal combiner 108, port 107_1 is connected to bandpass filter 405_1,port 107_2 is connected to bandpass filter 405_2, and port 107_N isconnected to bandpass filter 405_N. Each port 107_1 through 107_N isconnected to one end of its own bandpass filter 405_1 through bandpassfilter 405_N. The other end of the bandpass filter 405_1 through 405_Nis connected to a common port 109 via a common node 415. The common node415 can be a common connection point, a common transmission line, acommon wire, etc., as a mutual location for electrical connection. Thecommon port 109 connects to each bandpass filter 405_1 through bandpassfilter 405_N, while the individual ports 107_1 through 107_N areconnected (only) to their respective bandpass filter 405_1 throughbandpass filter 405_N.

Because the bandpass filters 405_1 through 405_N only transmitrespective reflected readout microwave signals 305_1 through 305_N inthe respective passband, the signal combiner 108 is configured such thateach bandpass filter 405_1 through bandpass filter 405_N covers adifferent band (or sub-band) of frequencies, such that none of thepassbands (of the bandpass filters 405) are overlapping. Accordingly,each port 107_1 through port 107_N is isolated from one another becauseof being connected to its respective bandpass filter 405_1 through405_N, such that no microwave signal 305 through any one port 107 leaksinto another port 107 via the common node 415. As such each port 107 isisolated from other ports 107 and is designed to transmit its ownmicrowave signal 305 at a predefined frequency (or within a predefinedfrequency band), as a result of being connected to its own bandpassfilter 405. Accordingly, the bandpass filters 405_1 through 405_N areresponsible for providing the isolation among ports 107-1 through 107_N.

The respective ports 107, bandpass filters 405, common node 415, andcommon port 109 are connected to one another via transmission lines 30.The transmission line 30 can be a stripline, microstrip, coplanarwaveguide, etc. The microwave bandpass filters 405 are designed andimplemented using lossless or low loss lumped elements such assuperconducting inductors, superconducting gap capacitors and/or platecapacitors, passive superconducting elements. The superconductingelements include lumped-element inductors, meander lines, kineticinductance lines, gap capacitors, interdigitated capacitors, and/orplate capacitors (with low loss dielectrics). Other possibleimplementations of the bandpass filters include coupled-line filters,and/or capacitively-coupled series resonators.

The signal combiner 108 is configured with the frequency relation f₁<f₂<. . . <f_(N), where each frequency f₁, f₂, . . . f_(N) is the centerfrequency of the bandpass filters 405_1 through 405_N, respectively. Thesignal combiner 108 is configured such that it satisfies the inequality

$\frac{{BW}_{j} + {BW}_{i}}{2} < {{f_{j} - f_{i}}}$

where i, j=1, 2, . . . N and j≠i. This inequality requires that thefrequency spacing between the center frequencies of each pair ofbandpass filters exceeds their average bandwidths. In other words, theinequality ensures that none of the bandpass filters have overlappingbandwidths (i.e., frequency range). As an example, one bandpass filter405 can have a passband of 1 megahertz (MHz), another bandpass filter405 can have a passband of 10 MHz, yet another bandpass filter 405 canhave a passband of 100 MHz, and so forth.

FIG. 5 is a schematic of the signal combiner 108 for quantum signalsaccording to embodiments. The signal combiner 108 includes all thevarious features discussed herein. Further, the signal combiner 108includes additional features to ensure impedance matching for passingmicrowave signals (i.e., minimize reflections along the signal path),and also to enable the connection of multiple branches/lines to thecommon node 415.

In FIG. 5, impedance transformers 505_1 through 505_N are respectivelyadded between the respective ports 107_1 through 107_N and theirassociated bandpass filters 405_1 through 405_N. Also, the signalcombiner 108 includes a wideband impedance transformer 510 connected tothe common node 415 and the common port 109. The impedance transformers505_1 through 505_N and impedance transformer 510 are configured toprovide impedance matching. On one end of the signal combiner 108, theimpedance transformers 505_1 through 505_N are structured to match (ornearly match) the input impedance Z₀ of the ports 107_1-107_N and tomatch the characteristic impedance associated with bandpass filter 405_1through 405_N. Each of the impedance transformers 505_1 through 505_N isconfigured with a characteristic impedance Z=√{square root over(Z₀Z_(H))}, where Z₀ is the input impedance (as well as the outputimpedance), where Z_(H) is the high impedance of the bandpass filters405_1 through 405_N, and where Z is the impedance of each impedancetransformers 505_1 through 505_N. The average characteristic impedance Zis the square root of the product of Z₀ and Z_(H). Each of the impedancematching transformers 505_1 through 505_N has a length according to itsown respective relationship λ₁/4, λ₂/4, . . . , λ_(N)/4, where λ₁ is thewavelength of the microwave signal 305_1, where λ₂ is wavelength of themicrowave signal 305_2, through λ_(N) which is the wavelength of themicrowave signal 305_N. These impedance transformers have in generalnarrow bandwidths. One reason why transforming the impedance of thedevice ports Z₀ to high characteristic impedance Z_(H) in the region ofthe common node can be useful is because, in general, high impedancetransmission lines, such as a microstrip or stripline, have narrowtraces which in turn minimize the physical size of the common node andallows more lines to be joined together at that node. This isparticularly relevant if the bandpass filters are implemented ascoupled-line filters and/or capacitively-coupled resonators. If,however, all bandpass filters are implemented using lumped-elements(with a very small footprint), such impedance transformations might beneeded less.

In one implementation, the impedance transformers 505_1 through 505_Ncan be impedance matching transmission lines, i.e., tapered, where oneend has a wide width matching the input impedance Z₀ and the oppositeend has a narrow width matching the high impedance Z_(H) of the bandpassfilters 405.

In one implementation, the wideband impedance transformer 510 can be animpedance matching transmission line where one end has a narrow widthmatching the high impedance Z_(H) of the bandpass filters 405 (viacommon node 415) while the opposite end has a wide width matching theoutput impedance Z₀. Such a wideband impedance transformer 510 can beimplemented using tapered transmission lines, for example, transmissionlines whose widths are changed adiabatically on the scale of the maximumsignal wavelength. Other implementations of tapered lines known to oneskilled in the art are possible as well, such as the Exponential Taperor the Klopfenstein Taper. Also, it should be noted that the widebandrequirement for this impedance transformer versus the other transformers505 arises from the fact that this wideband transformer 510 needs tomatch the characteristic impedance for a wideband of signal frequenciestransmitted through it, in contrast to the impedance transformers 505which need only to match the impedance for a narrow frequency rangecentered around the corresponding center frequency of the respectivebandpass.

FIG. 5 illustrates one particular example for impedance matching, and itshould be appreciated that the general scheme of the combiner 108 is notlimited to this particular implementation. For example, in someimplementations, the bandpass filters 405 can have the samecharacteristic impedance as the port Z₀ (107), and impedancetransformers are incorporated between the bandpass filters 405 and thehigh impedance Z_(H) connecting to the common node 109.

The impedance designation Z₀ is the characteristic impedance at ports107_1 through 107_N and port 109 (which can be the input and outputports). For example, the characteristic impedance Z₀ can be 50 ohms (Ω)at each ports 107 and 109 as recognized by one skilled in the art.

It should be noted that N represents the last of each of thefrequencies, microwave signals 305, bandpass filters 405, and theimpedance transformers 505_N. Also, N represents the last ofqubit-resonator systems 102, readout resonators 152, qubits 154,directional couplers 104, diplexers 106, and so forth.

The circuit elements of the circuit 100 can be made of superconductingmaterial. The respective ports 107, bandpass filters 405, common node415, common port 109, impedance transformers 505, and transmission lines30 are made of superconducting materials. Additionally, thequbit-resonator systems 102, readout resonators 152, qubits 154,directional couplers 104, diplexers 106, amplifier 110, and circulator112 are made of superconducting materials. Examples of superconductingmaterials (at low temperatures, such as about 10-100 millikelvin (mK),or about 4 K) include niobium, aluminum, tantalum, etc. For example, theJosephson junctions are made of superconducting material, and theirtunnel junctions can be made of a thin tunnel barrier, such as an oxide.The capacitors can be made of superconducting material separated bylow-loss dielectric material. The transmission lines (i.e., wires)connecting the various elements are made of a superconducting material.

FIG. 6 is a flow chart 600 of a method of forming an integrated driveand readout circuit/assembly 100 according to embodiments. The methodincludes providing directional couplers 104_1 through 104_N configuredto connect to qubit-resonator systems 102_1 through 102_N respectivelyat block 602, connecting diplexers 106_1 to the directional couplers104_1 through 104_N respectively at block 604, and connecting amicrowave signal combiner 108 to each of the diplexers 106_1 through106_N at block 606.

Each of the directional couplers 104_1 through 104_N includes a firstport, a second port, a third port, and a fourth port. The first port103A is configured to receive a qubit signal and a readout signal, thesecond port 103B is connectable to the qubit-resonator systems 102_1through 102_N, the third port 103C is connectable to the diplexers 106_1through 106_N, and the fourth port 103D is an isolated port.

The diplexers 106_1 through 106_N each include a low-pass filter port105B, a high-pass filter port 105C, and a common port (C) 105A. Thecommon port is configured to support both low and high frequency bandsassociated with the low-pass-band port and high-pass-band portrespectively. The common port 105A of the diplexers 106_1 through 106_Nis connected to the directional couplers 104_1 through 104_Nrespectively.

The diplexers 106_1 through 106_N are configured to direct a reflecteddrive microwave signal to the low-pass filter port 105B, where thelow-pass filter port 105B is connected to a termination point (e.g., 50Ωtermination). The high-pass filter port 105C is connected to the signalcombiner 108. The microwave signal combiner 108 is configured to combinemicrowave signals from each the diplexers 106_1 through 106_N asdepicted in FIG. 1. The microwave signal combiner 108 is configured tooutput combined microwave signals (e.g., combined microwave signalshaving frequencies f₁ through f_(N)) to a quantum-limited amplifier 110.The quantum-limited amplifier 110 is configured to amplify the combinedmicrowave signals and output the combined microwave signals to acirculator 112.

FIG. 7 is flow chart 700 of a method of driving qubit-resonator systems102_1 through 102_N according to embodiments. The method includestransmitting, by directional couplers 104_1 through 104_N, (drive)microwave signals (at the qubit resonance frequencies f_(q1) throughf_(qN)) to the qubit-resonator systems 102_1 through 102_N respectively(at block 702), receiving, by the directional couplers 104_1 through104_N, reflected (drive) microwave signals (at the qubit resonancefrequencies f_(q1) through f_(qN)) from the qubit-resonator systems102_1 through 102_N (at block 704), and receiving, by the diplexers106_1 through 106_N, the transmitted (drive) microwave signals from thedirectional couplers 104_1 through 104_N respectively (at block 706). Inother words, the reflected signals off the qubit-resonator systems 102_1through 102_N get transmitted through the directional coupler 104_1through 104_N. The diplexers 106_1 through 106_N are configured todirect the reflected (drive) microwave signals (at the qubit resonancefrequencies f_(q1) through f_(qN)) to a terminated port (e.g., 50Ω coldtermination).

FIG. 8 is a flow chart 800 of a method of reading out qubit-resonatorsystems (i.e., inferring the state of superconducting qubits 154_1through 154_N by reading out the readout resonators 152_1 through 152_Nrespectively) according to embodiments. The method includestransmitting, by directional couplers 104_1 through 104_N, (readout)microwave signals (at the readout resonance frequencies f₁ throughf_(N)) to the qubit-resonator systems 102_1 through 102_N respectively(at block 802), and receiving, by the directional couplers 104_1 through104_N, reflected (readout) microwave signals (at the readout resonancefrequencies f₁ through f_(N)) from the qubit-resonator systems 102_1through 102_N respectively (at block 804). Also, the method includesreceiving, by the diplexers 106_1 through 106_N, the transmitted readoutmicrowave signals (at the readout resonance frequencies f₁ throughf_(N)) through the directional couplers 104_1 through 104_N respectively(at block 806), and receiving, by the microwave signal combiner 108, thetransmitted readout microwave signals (at the readout resonancefrequencies f₁ through f_(N)) from the diplexers 106_1 through 106_Nrespectively (at block 808). It is noted that the transmitted readoutmicrowave signals (at the readout resonance frequencies f₁ throughf_(N)) were previously reflected (readout) microwave signals (at thereadout resonance frequencies f₁ through f_(N)) from the qubit-resonatorsystems 102_1 through 102_N.

The microwave signal combiner 108 is configured to combine the multipletransmitted readout microwave signals into multiple microwave signals(at the readout frequencies f₁ through f_(N)). Further, the methodinclude transmitting, by the microwave signal combiner 108, the combinedreadout microwave signals (including the readout resonance frequenciesf₁ through f_(N)) to a quantum-limited amplifier 110 (at block 810).

Technical effects and benefits include methods and structures for ascalable qubit drive and readout circuit. These structures that can befully integrated on a chip or a printed circuit board. Technicaladvantages include minimizing the number of output and control lines.Additionally, technical effects and benefits include a structure thathas lighter weight, can be thermalized better, and has smaller footprintthan schemes which incorporate commercial cryogenic circulators andisolators

The term “about” and variations thereof are intended to include thedegree of error associated with measurement of the particular quantitybased upon the equipment available at the time of filing theapplication. For example, “about” can include a range of ±8% or 5%, or2% of a given value.

The flowchart and block diagrams in the Figures illustrate thearchitecture, functionality, and operation of possible implementationsof systems, methods, and computer program products according to variousembodiments of the present invention. In this regard, each block in theflowchart or block diagrams can represent a module, segment, or portionof instructions, which includes one or more executable instructions forimplementing the specified logical function(s). In some alternativeimplementations, the functions noted in the block can occur out of theorder noted in the figures. For example, two blocks shown in successioncan, in fact, be executed substantially concurrently, or the blocks cansometimes be executed in the reverse order, depending upon thefunctionality involved. It will also be noted that each block of theblock diagrams and/or flowchart illustration, and combinations of blocksin the block diagrams and/or flowchart illustration, can be implementedby special purpose hardware-based systems that perform the specifiedfunctions or acts or carry out combinations of special purpose hardwareand computer instructions.

The descriptions of the various embodiments of the present inventionhave been presented for purposes of illustration, but are not intendedto be exhaustive or limited to the embodiments discussed. Manymodifications and variations will be apparent to those of ordinary skillin the art without departing from the scope and spirit of the describedembodiments. The terminology used herein was chosen to best explain theprinciples of the embodiments, the practical application or technicalimprovement over technologies found in the marketplace, or to enableothers of ordinary skill in the art to understand the embodimentsdiscussed herein.

What is claimed is:
 1. A method of driving at least one qubit-resonatorsystem, the method comprising: transmitting, via a circuit, a drivesignal to the at least one qubit-resonator system; receiving, via thecircuit, the drive signal having been reflected from the at least onequbit-resonator system; and directing, via the circuit, the drive signalhaving been reflected to a termination.
 2. The method of claim 1,wherein the circuit is configured to terminate any other drive signalhaving been reflected from any other qubit-resonator system.
 3. Themethod of claim 1, wherein the circuit is configured to terminatesignals above a predefined frequency which have been reflected from theat least one qubit-resonator system.
 4. The method of claim 1, whereinthe circuit is configured to pass signals above a predefined frequency,such that the signals are passed to a combiner in the circuit.
 5. Themethod of claim 1, wherein the circuit includes a directional coupler.6. The method of claim 5, wherein the directional coupler transmits thedrive signal to the at least one qubit-resonator system.
 7. The methodof claim 1, wherein the circuit includes a diplexer.
 8. The method ofclaim 7, wherein the diplexer receives the drive signal having beenreflected from the at least one qubit-resonator system.
 9. The method ofclaim 8, wherein the diplexer terminates the drive signal having beenreflected from the at least one qubit-resonator system, therebypreventing transmission of the drive signal to a signal combiner. 10.The method of claim 8, wherein the diplexer passes any signal above apredefined frequency to a signal combiner.
 11. A method of reading outat least one qubit-resonator system, the method comprising:transmitting, via a circuit, a readout signal to the at least onequbit-resonator system; receiving, via the circuit, the readout signalhaving been reflected from the at least one qubit-resonator system; anddirecting the readout signal having been reflected to be with at leastone other reflected readout signal.
 12. The method of claim 11, whereinthe readout signal is combined with the at least one other reflectedreadout signal.
 13. The method of claim 11, wherein the readout signalis combined with the at least one other reflected readout signal using asignal combiner of the circuit.
 14. The method of claim 11, wherein thereadout signal is combined with the at least one other reflected readoutsignal into combined signals.
 15. The method of claim 14, furthercomprising transmitting the combined signals to an amplifier.
 16. Themethod of claim 15, wherein the amplifier receives the combined signalsfrom a signal combiner.
 17. The method of claim 15, wherein theamplifier is a quantum-limited amplifier.
 18. The method of claim 11,wherein any signal above a predefined frequency is not directed to bewith the at least one other reflected readout signal.
 19. The method ofclaim 11, wherein a diplexer receives the readout signal having beenreflected from the at least one qubit-resonator system.
 20. The methodof claim 19, wherein the diplexer directs the readout signal having beenreflected to be with the at least one other reflected readout signal ata signal combiner.